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6.15. FLAME PROPAGATION IN HYDROGEN-BROMINE MIXTURES 187
6.15 Flame propagation in Hydrogen-Bromine mixtures
The present example contains a calculation of the velocity of the hydrogen-bromine
flame performed with a variation of the method developed by von Kármán and Penner
[40]. The method presented here differs from earlier calculations because the
influence of dissociation of bromine on the flame velocity is evaluated properly. Von
Kármán and Penner included the influence of the atoms of bromine on the reaction
rate but when calculating the distribution of the mole fraction of Br 2 , H 2 and HBr,
they neglected the mole fraction of Br atoms. However, for temperatures close to the
maximum flame temperature the dissociation of Br 2 reduces substantially the value
for the mole fraction of Br 2 , which has an important influence on the flame velocity.
Hence it seemed desirable to compute the burning velocity correctly, especially
in hydrogen-rich flames where the influence of dissociation is most important. Von
Kármán and Penner also neglect the influence of the energy of dissociation of Br 2 ,
which should be taken into account since it may be of the same order of magnitude as
the energy transferred by convection through the flame.
In the following, a method is developed for the correct calculation of the mole
fraction of Br 2 and of the influence of its dissociation energy on the velocity of the
flame, within the limitations of the steady-state assumption for the distribution of
bromine and hydrogen atoms. This method will be applied to computation for the
four hydrogen-rich flames previously considered by von Kármán and Penner. The results
are compared with those obtained by these authors and are shown to differ by not
more than 25% even for the hottest flame.
A detailed study of the structure of the flame is also presented. It will be shown
that dissociation of Br 2 reduces the flame velocity because of a decrease in the number
of molecules of bromine which exist near the hot flame boundary. On the other hand,
it will be seen that the influence of the dissociation energy can be neglected if thermal
convection is ignored because these two effects tend to cancel.
The procedure developed here follows closely the work performed in Ref. [41]
and could also be useful for computations on other types of flames.
Flame Equations
Since there are only five different chemical components, namely, HBr, Br 2 , H 2 , Br
and H, the unknowns are:
1) Five flux fractions, ε i .